How much money to last me till I die?

My co-worker and I generally end the work day with random ideas and problem-solving. Yesterday we thought of a question that neither of us could figure out how to solve.

It’s a math problem. Hypothetically, I want to start with some amount of money that I can invest today, and spend 50,000 (2014, adjusted for inflation annually) dollars annually and then be broke the day I die. Say I live for another 60 years.

For our hypothetical situation, we decided to fix annual inflation at 3% and annual interest earned at 6%. How much money do I need to start with to spend $50,000 this year, and $294580.16 in 2074, and then die when I have zero dollars in my account?

Don’t need answer fast: this isn’t homework, it’s bored co-worker work.

In the US?

The cost of medicine is probably completely unpredictable. You get your neck broken in the wrong place tonight and you might have to pay unpredictable sums for decades.

$1,171,000.00

Yes, that is the real answer given your exact stipulations. I built an Excel spreadsheet to come up with the answer. You made a mistake in your OP. You need about $160,000 a year to match $50,000 a year now given 3% constant inflation. Also note that my number is correct mathematically speaking but it is way too low for the real world. You could easily see a less than 6% or even a negative return during the early years and that destroys the whole model.

Seed Money
$1,171,000.00

Year Spending per Year Investment Remaining
1 $50,000.00 $1,121,000.00
2 $51,000.00 $1,138,260.00
3 $52,020.00 $1,155,555.60
4 $53,060.40 $1,172,868.94
5 $54,121.61 $1,190,180.67
6 $55,204.04 $1,207,469.90
7 $56,308.12 $1,224,714.06
8 $57,434.28 $1,241,888.78
9 $58,582.97 $1,258,967.82
10 $59,754.63 $1,275,922.93
11 $60,949.72 $1,292,723.67
12 $62,168.72 $1,309,337.37
13 $63,412.09 $1,325,728.90
14 $64,680.33 $1,341,860.54
15 $65,973.94 $1,357,691.84
16 $67,293.42 $1,373,179.42
17 $68,639.29 $1,388,276.76
18 $70,012.07 $1,402,934.08
19 $71,412.31 $1,417,098.06
20 $72,840.56 $1,430,711.63
21 $74,297.37 $1,443,713.77
22 $75,783.32 $1,456,039.23
23 $77,298.98 $1,467,618.26
24 $78,844.96 $1,478,376.37
25 $80,421.86 $1,488,233.99
26 $82,030.30 $1,497,106.17
27 $83,670.91 $1,504,902.24
28 $85,344.32 $1,511,525.47
29 $87,051.21 $1,516,872.67
30 $88,792.23 $1,520,833.82
31 $90,568.08 $1,523,291.62
32 $92,379.44 $1,524,121.04
33 $94,227.03 $1,523,188.86
34 $96,111.57 $1,520,353.16
35 $98,033.80 $1,515,462.78
36 $99,994.48 $1,508,356.74
37 $101,994.37 $1,498,863.67
38 $104,034.25 $1,486,801.12
39 $106,114.94 $1,471,974.94
40 $108,237.24 $1,454,178.49
41 $110,401.98 $1,433,191.97
42 $112,610.02 $1,408,781.50
43 $114,862.22 $1,380,698.37
44 $117,159.47 $1,348,678.05
45 $119,502.66 $1,312,439.26
46 $121,892.71 $1,271,682.96
47 $124,330.56 $1,226,091.23
48 $126,817.18 $1,175,326.14
49 $129,353.52 $1,119,028.53
50 $131,940.59 $1,056,816.72
51 $134,579.40 $988,285.13
52 $137,270.99 $913,002.84
53 $140,016.41 $830,512.02
54 $142,816.74 $740,326.33
55 $145,673.07 $641,929.18
56 $148,586.53 $534,771.86
57 $151,558.26 $418,271.63
58 $154,589.43 $291,809.67
59 $157,681.22 $154,728.82
60 $160,834.84 $6,331.33

Alternatively, you could just win the lottery.

After all, lots of people do that. And …

You never can tell. And …

Shit happens.

$1,460,000.

Making the following assumption.
You take out $50,000 at the start of year (and at the start of the year from then on) one to make it through the year. If you take out the money at the end of the year it will be different.
.
Or, in the spirit of janelogin, $0 if you die at once.
Or much less if somewhere along the way you win the lottery.

You can go to an insurance company and buy an annuity to pay out exactly the amount you described.

Shagnasty, I don’t think your numbers work out.

$51,000 is not a 3% increase from $50,000, it is a 2% increase. Your whole first column seems based on 2% rather than 3%. 3% inflation on $50k for 60 years does come to $286,000.14 in 60 years (2073 is the 60th year, not 2074).

Given that difference, the answer comes out to $1,360,330 with -$0.57 left at the end.
Roddy

eta: SandyHook is right that it makes a difference if you take the money out at the beginning of the year. In that case I come up with $1,451,140 to start.

This is probably the best basic calculator I’ve ever seen.

http://www.nbcnews.com/id/21563675/ns/business-your_retirement/ns/business-your_retirement/t/retirement-calculator/#.UgsL79K-o_y

Which has nothing at all to do with the question that was asked.

The three crucial assumptions are inflation, investment return and mortality. And in fact you can reduce the first two assumptions to just one; the gap between inflaction and investment return.

But, if you’re doing this calculation for an individual, mortality is far and away the most signficant assumption,and also the one that it’s near-impossible to get right. Which is why, in the real world, if you actually want an income guaranteed as to amount, and as to enduring for life, the rational course is to pool your mortality risk with others having the same objective, and buy an annuity from a life office.

You are absolutely right even if 3% inflation is fairly high based on current trends. My mistake. That will teach me to throw spreadsheets together in 5 minutes or less. I agree with your numbers. I still say that even $1.45 million dollars isn’t enough to do this experiment safely in the real world unless you are super-frugal and have an almost continuous string of good luck. I think you need at least a $500,000 or more cushion in there to cover any uncertainties. Even then, you aren’t going to be living the high life for 60 years even though you are technically a multi-millionaire for most of it.

I assume this is $50,000 before taxes?
And these are investments you can make that would not require payment of taxes along the way?

Try this online calculator - http://www.firecalc.com/ - you will have to play around with some of the parameters.

Using the ‘Investigate’ tab, setting portfolio performance to 6% (and defaults for all others) it reported:

I just set up a spread sheet using a monthly calculation, instead of a yearly.
If I got with a payout at the beginning of the month, and add in interest at the end of the month, then I get a value of $1,392,784, with $31 left in the bank at the end. And for that final year (year 30) the total payout is $297,698.

There is no way that math could be correct. The lowest possible average with that high and low mark would be 25774.02 (one cycle at 1.5MM and the other 60 at 276). You would have to run well over 70,000 cycles with one at 1.5MM and the rest at 276 before you even begin to approach that average!

Well, how much for the annuity?

Too much. An annuity is a terrible investment, unless of course you’re selling them. The comissions are huge, and they come off the top.

It’s not surprising that the various “answers” equate to about 25-30 times $50,000, give or take. It’s long been accepted that 4.0% is a realistic “safe withdrawal rate” if you want your money to last the rest of your life. So, divide $50,000 by 0.04 and you get $1,250,000. Given recent low interest rates, some people argue that you should really only take out 3.5% or even 3.0% as a safe withdrawal rate, meaning you would have to have $1.43 million or even $1.67 million to take out $50k and increase it by inflation. I think 3.0% is too conservative. But these numbers definitely put you in the ballpark, and are figures people use to figure out when they have “hit their number” to retire.

Not necessarily. Yes, commissions and fees are high, but an annuity can still be wise for someone who wants guaranteed income for the rest of his life, and isn’t worried about passing wealth to heirs. There are various annuity calculators online, and you can easily see what kind of payouts you can receive given a lump-sum investment. The payouts are quite a bit higher than the 3.5 to 4.0 percent safe withdrawal rates being discussed. Of course, the downside is if you die in just a few years there is no money to pass on to heirs. That’s where the insurance companies really make money from annuities.

4% is generally used for people retiring at about 65. The OP refers to wanting the money to last 60 years. The withdrawal rate for that length of time is more like 3.5% (and indexed by inflation each year).

I agree with you about 3% being too conservative. Over on bogleheads.org they are so conservative that people talk about 2.5% or even 2%. I’d like to be an heir of theirs.